LMI-based linear parameter varying PID control design and its application to an aircraft control system

To bridge the gap between real-world applications and theoretical achievements, this paper proposes a new synthesis approach of gain-scheduled proportional–integral–derivative (PID) control for linear parameter-varying (LPV) systems. It is recognized that the synthesis problem of PID controllers for LPV systems should be formulated as nonconvex optimization problems. To avoid this situation, using a special matrix transformation, novel synthesis conditions with linear matrix inequality constraints are provided in this paper. The stability of the resulting closed-loop system is guaranteed theoretically based on a parameter-dependent Lyapunov function, and two types of robust performance (bounded $$L_2$$ norm and induced $$L_2$$ norm) are also achieved in the corresponding synthesis conditions. Then, the control system of aircraft is designed based on the proposed method, and the system responses are compared with the traditional LPV-PID control and the LPV dynamic output feedback control.

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